Abstract
We construct here, forl=2g 2 +2g+1 or2g 2 +3g+1, a family with one parameter of hyperelliptic curves of genusg overQ such that its jacobian has a point of orderl rational overQ(t). Wheng=2 the method allows to construct, forl=17, 19 or 21 a family with one parameter of hyperelliptic curves of genus 2 overQ such that its jacobian has a point of orderl rational overQ(t).
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Leprévost, F. Torsion sur des familles de courbes de genre g. Manuscripta Math 75, 303–326 (1992). https://doi.org/10.1007/BF02567087
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DOI: https://doi.org/10.1007/BF02567087